Southwest's WiFi service is $8 per day (not per flight segment), per device, on WiFi-enabled aircraft, including stops and connections.
By now, most Southwest aircraft (maybe all of them) are WiFi-enabled. To make sure you'll be on WiFi-enabled aircraft, visit Southwest's "WiFi Finder" within 24 hours of your flight departure: http://www.southwest.com/html/air/products/wifi-access.html
However, unlike most other airlines operating in the United States, Southwest has not chosen to install any kind of power outlets for electronic devices at seats -- not 110V AC, not 12-15V DC receptacles, and not USB. So make sure your device is fully charged.
When I flew to Florida 2 weeks ago, our SW plane did not have wifi.
It did on the way home, I had downloaded the player the day before, I got an email from them the day before. I watched the free TV channels, worked well.